Abstract

We report simultaneous generation of multiple conical second-harmonic waves in a two-dimensional nonlinear photonic structure when illuminated by two overlapping noncollinear fundamental beams. We show that this phenomenon is caused by the nonlinear Čerenkov radiation emitted due to the interaction of photons from each constituent fundamental beam as well as the virtual one propagating along the bisector of the two beams. In addition, by studying the asymmetric geometry of the interaction, we uniquely verify the effects of reciprocal vectors on the Čerenkov-type second-harmonic generation in nonlinear photonic structures.

© 2010 Optical Society of America

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  1. J. A. Amstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
    [CrossRef]
  2. M. Houe and P. D. Townsend, J. Phys. D 28, 1747 (1995).
    [CrossRef]
  3. V. Berger, Phys. Rev. Lett. 81, 4136 (1998).
    [CrossRef]
  4. N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, Phys. Rev. Lett. 84, 4345(2000).
    [CrossRef] [PubMed]
  5. A. Arie and N. Voloch, Laser Photon. Rev. 4, 355 (2010).
    [CrossRef]
  6. A. Zembrod, H. Puell, and J. Giordmaine, Opt. Quantum Electron. 1, 64 (1969).
    [CrossRef]
  7. S. M. Saltiel, Y. Sheng, N. Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE J. Quantum Electron. 45, 1465 (2009).
    [CrossRef]
  8. Y. Sheng, S. M. Saltiel, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, Opt. Lett. 35, 1317 (2010).
    [CrossRef] [PubMed]
  9. Y. Zhang, F. Wang, K. Geren, S. N. Zhu, and M. Xiao, Opt. Lett. 35, 178 (2010).
    [CrossRef] [PubMed]
  10. Y. Sheng, A. Best, H. Butt, W. Krolikowski, A. Arie, and K. Koynov, Opt. Express 18, 16539 (2010).
    [CrossRef] [PubMed]
  11. A. Fragemann, V. Pasiskevicus, and F. Laurell, Appl. Phys. Lett. 85, 375 (2004).
    [CrossRef]
  12. X. Deng and X. Chen, Opt. Express 18, 15597 (2010).
    [CrossRef] [PubMed]
  13. V. Roppo, D. Dumay, J. Trull, C. Cojocaru, S. M. Saltiel, K. Staliunas, R. Vilaseca, D. N. Neshev, W. Krolikowski, and Y. S. Kivshar, Opt. Express 16, 14192 (2008).
    [CrossRef] [PubMed]
  14. S. M. Saltiel, D. N. Neshev, W. Krolikowski, R. Fisher, A. Arie, and Y. S. Kivshar, Phys. Rev. Lett. 100, 103902 (2008).
    [CrossRef] [PubMed]
  15. S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Y. S. Kivshar, Phys. Rev. Lett. 104, 083902 (2010).
    [CrossRef] [PubMed]
  16. I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, Appl. Phys. B 96, 423 (2009).
    [CrossRef]

2010 (6)

2009 (2)

I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, Appl. Phys. B 96, 423 (2009).
[CrossRef]

S. M. Saltiel, Y. Sheng, N. Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

2008 (2)

2004 (1)

A. Fragemann, V. Pasiskevicus, and F. Laurell, Appl. Phys. Lett. 85, 375 (2004).
[CrossRef]

2000 (1)

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, Phys. Rev. Lett. 84, 4345(2000).
[CrossRef] [PubMed]

1998 (1)

V. Berger, Phys. Rev. Lett. 81, 4136 (1998).
[CrossRef]

1995 (1)

M. Houe and P. D. Townsend, J. Phys. D 28, 1747 (1995).
[CrossRef]

1969 (1)

A. Zembrod, H. Puell, and J. Giordmaine, Opt. Quantum Electron. 1, 64 (1969).
[CrossRef]

1962 (1)

J. A. Amstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Amstrong, J. A.

J. A. Amstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Arie, A.

A. Arie and N. Voloch, Laser Photon. Rev. 4, 355 (2010).
[CrossRef]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Y. S. Kivshar, Phys. Rev. Lett. 104, 083902 (2010).
[CrossRef] [PubMed]

Y. Sheng, S. M. Saltiel, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, Opt. Lett. 35, 1317 (2010).
[CrossRef] [PubMed]

Y. Sheng, A. Best, H. Butt, W. Krolikowski, A. Arie, and K. Koynov, Opt. Express 18, 16539 (2010).
[CrossRef] [PubMed]

I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, Appl. Phys. B 96, 423 (2009).
[CrossRef]

S. M. Saltiel, Y. Sheng, N. Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, R. Fisher, A. Arie, and Y. S. Kivshar, Phys. Rev. Lett. 100, 103902 (2008).
[CrossRef] [PubMed]

Bang, O.

S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Y. S. Kivshar, Phys. Rev. Lett. 104, 083902 (2010).
[CrossRef] [PubMed]

Berger, V.

V. Berger, Phys. Rev. Lett. 81, 4136 (1998).
[CrossRef]

Best, A.

Bloch, N.

S. M. Saltiel, Y. Sheng, N. Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

Bloembergen, N.

J. A. Amstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Broderick, N. G. R.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, Phys. Rev. Lett. 84, 4345(2000).
[CrossRef] [PubMed]

Butt, H.

Chen, X.

Cojocaru, C.

Deng, X.

Dolev, I.

I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, Appl. Phys. B 96, 423 (2009).
[CrossRef]

Ducuing, J.

J. A. Amstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Dumay, D.

Fisher, R.

S. M. Saltiel, D. N. Neshev, W. Krolikowski, R. Fisher, A. Arie, and Y. S. Kivshar, Phys. Rev. Lett. 100, 103902 (2008).
[CrossRef] [PubMed]

Fragemann, A.

A. Fragemann, V. Pasiskevicus, and F. Laurell, Appl. Phys. Lett. 85, 375 (2004).
[CrossRef]

Gadret, G.

I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, Appl. Phys. B 96, 423 (2009).
[CrossRef]

Ganany-Padowicz, A.

I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, Appl. Phys. B 96, 423 (2009).
[CrossRef]

Gayer, O.

I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, Appl. Phys. B 96, 423 (2009).
[CrossRef]

Geren, K.

Giordmaine, J.

A. Zembrod, H. Puell, and J. Giordmaine, Opt. Quantum Electron. 1, 64 (1969).
[CrossRef]

Hanna, D. C.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, Phys. Rev. Lett. 84, 4345(2000).
[CrossRef] [PubMed]

Houe, M.

M. Houe and P. D. Townsend, J. Phys. D 28, 1747 (1995).
[CrossRef]

Kivshar, Y. S.

S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Y. S. Kivshar, Phys. Rev. Lett. 104, 083902 (2010).
[CrossRef] [PubMed]

Y. Sheng, S. M. Saltiel, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, Opt. Lett. 35, 1317 (2010).
[CrossRef] [PubMed]

S. M. Saltiel, Y. Sheng, N. Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, R. Fisher, A. Arie, and Y. S. Kivshar, Phys. Rev. Lett. 100, 103902 (2008).
[CrossRef] [PubMed]

V. Roppo, D. Dumay, J. Trull, C. Cojocaru, S. M. Saltiel, K. Staliunas, R. Vilaseca, D. N. Neshev, W. Krolikowski, and Y. S. Kivshar, Opt. Express 16, 14192 (2008).
[CrossRef] [PubMed]

Koynov, K.

Krolikowski, W.

S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Y. S. Kivshar, Phys. Rev. Lett. 104, 083902 (2010).
[CrossRef] [PubMed]

Y. Sheng, S. M. Saltiel, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, Opt. Lett. 35, 1317 (2010).
[CrossRef] [PubMed]

Y. Sheng, A. Best, H. Butt, W. Krolikowski, A. Arie, and K. Koynov, Opt. Express 18, 16539 (2010).
[CrossRef] [PubMed]

S. M. Saltiel, Y. Sheng, N. Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, R. Fisher, A. Arie, and Y. S. Kivshar, Phys. Rev. Lett. 100, 103902 (2008).
[CrossRef] [PubMed]

V. Roppo, D. Dumay, J. Trull, C. Cojocaru, S. M. Saltiel, K. Staliunas, R. Vilaseca, D. N. Neshev, W. Krolikowski, and Y. S. Kivshar, Opt. Express 16, 14192 (2008).
[CrossRef] [PubMed]

Laurell, F.

A. Fragemann, V. Pasiskevicus, and F. Laurell, Appl. Phys. Lett. 85, 375 (2004).
[CrossRef]

Mangin, J.

I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, Appl. Phys. B 96, 423 (2009).
[CrossRef]

Neshev, D. N.

S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Y. S. Kivshar, Phys. Rev. Lett. 104, 083902 (2010).
[CrossRef] [PubMed]

S. M. Saltiel, Y. Sheng, N. Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, R. Fisher, A. Arie, and Y. S. Kivshar, Phys. Rev. Lett. 100, 103902 (2008).
[CrossRef] [PubMed]

V. Roppo, D. Dumay, J. Trull, C. Cojocaru, S. M. Saltiel, K. Staliunas, R. Vilaseca, D. N. Neshev, W. Krolikowski, and Y. S. Kivshar, Opt. Express 16, 14192 (2008).
[CrossRef] [PubMed]

Offerhaus, H. L.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, Phys. Rev. Lett. 84, 4345(2000).
[CrossRef] [PubMed]

Pasiskevicus, V.

A. Fragemann, V. Pasiskevicus, and F. Laurell, Appl. Phys. Lett. 85, 375 (2004).
[CrossRef]

Pershan, P. S.

J. A. Amstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Puell, H.

A. Zembrod, H. Puell, and J. Giordmaine, Opt. Quantum Electron. 1, 64 (1969).
[CrossRef]

Richardson, D. J.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, Phys. Rev. Lett. 84, 4345(2000).
[CrossRef] [PubMed]

Roppo, V.

Ross, G. W.

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, Phys. Rev. Lett. 84, 4345(2000).
[CrossRef] [PubMed]

Saltiel, S. M.

S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Y. S. Kivshar, Phys. Rev. Lett. 104, 083902 (2010).
[CrossRef] [PubMed]

Y. Sheng, S. M. Saltiel, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, Opt. Lett. 35, 1317 (2010).
[CrossRef] [PubMed]

S. M. Saltiel, Y. Sheng, N. Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, R. Fisher, A. Arie, and Y. S. Kivshar, Phys. Rev. Lett. 100, 103902 (2008).
[CrossRef] [PubMed]

V. Roppo, D. Dumay, J. Trull, C. Cojocaru, S. M. Saltiel, K. Staliunas, R. Vilaseca, D. N. Neshev, W. Krolikowski, and Y. S. Kivshar, Opt. Express 16, 14192 (2008).
[CrossRef] [PubMed]

Sheng, Y.

Staliunas, K.

Townsend, P. D.

M. Houe and P. D. Townsend, J. Phys. D 28, 1747 (1995).
[CrossRef]

Trull, J.

Vilaseca, R.

Voloch, N.

A. Arie and N. Voloch, Laser Photon. Rev. 4, 355 (2010).
[CrossRef]

Voloch-Bloch, N.

S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Y. S. Kivshar, Phys. Rev. Lett. 104, 083902 (2010).
[CrossRef] [PubMed]

Wang, F.

Xiao, M.

Zembrod, A.

A. Zembrod, H. Puell, and J. Giordmaine, Opt. Quantum Electron. 1, 64 (1969).
[CrossRef]

Zhang, Y.

Zhu, S. N.

Appl. Phys. B (1)

I. Dolev, A. Ganany-Padowicz, O. Gayer, A. Arie, J. Mangin, and G. Gadret, Appl. Phys. B 96, 423 (2009).
[CrossRef]

Appl. Phys. Lett. (1)

A. Fragemann, V. Pasiskevicus, and F. Laurell, Appl. Phys. Lett. 85, 375 (2004).
[CrossRef]

IEEE J. Quantum Electron. (1)

S. M. Saltiel, Y. Sheng, N. Bloch, D. N. Neshev, W. Krolikowski, A. Arie, K. Koynov, and Y. S. Kivshar, IEEE J. Quantum Electron. 45, 1465 (2009).
[CrossRef]

J. Phys. D (1)

M. Houe and P. D. Townsend, J. Phys. D 28, 1747 (1995).
[CrossRef]

Laser Photon. Rev. (1)

A. Arie and N. Voloch, Laser Photon. Rev. 4, 355 (2010).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Opt. Quantum Electron. (1)

A. Zembrod, H. Puell, and J. Giordmaine, Opt. Quantum Electron. 1, 64 (1969).
[CrossRef]

Phys. Rev. (1)

J. A. Amstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Phys. Rev. 127, 1918 (1962).
[CrossRef]

Phys. Rev. Lett. (4)

V. Berger, Phys. Rev. Lett. 81, 4136 (1998).
[CrossRef]

N. G. R. Broderick, G. W. Ross, H. L. Offerhaus, D. J. Richardson, and D. C. Hanna, Phys. Rev. Lett. 84, 4345(2000).
[CrossRef] [PubMed]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, R. Fisher, A. Arie, and Y. S. Kivshar, Phys. Rev. Lett. 100, 103902 (2008).
[CrossRef] [PubMed]

S. M. Saltiel, D. N. Neshev, W. Krolikowski, N. Voloch-Bloch, A. Arie, O. Bang, and Y. S. Kivshar, Phys. Rev. Lett. 104, 083902 (2010).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

(a) Domain pattern of the 2D NPS. (b) Schematic of the experiment. (c), (e) Images of the SH rings observed with the asymmetric ( δ 0 ) and symmetric ( δ = 0 ) FBs, respectively. (d), (f) Corresponding phase-matching diagrams.

Fig. 2
Fig. 2

Dependence of Čerenkov SH emission angles as a function of (a) the sample orientation angle δ and (b) the wavelength of the FBs. The squares, triangles, and circles refer to the SH waves emitted by the individual FBs and the virtual beam, respectively. The solid curves are the theoretic predictions from Eqs. (1, 2, 3).

Fig. 3
Fig. 3

(a) Schematic of the phase-matching condition for a noncollinear fundamental beam. (b) Theoretically predicted intensity distribution of Čerenkov SHG obtained by I 2 g ˜ 2 .

Fig. 4
Fig. 4

(a) SH pattern observed when the FBs cross outside the sample. (b) Corresponding interaction geometry.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

| k 2 | cos θ 2 = 2 | k 1 | cos θ 1 ,
| k 2 | cos θ 2 = 2 | k 1 | cos θ 1 ,
| k 2 | cos θ 2 = | k 1 | ( cos θ 1 + cos θ 1 ) .

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